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slarrv.f(3)				      LAPACK				      slarrv.f(3)

NAME
       slarrv.f -

SYNOPSIS
   Functions/Subroutines
       subroutine slarrv (N, VL, VU, D, L, PIVMIN, ISPLIT, M, DOL, DOU, MINRGP, RTOL1, RTOL2, W,
	   WERR, WGAP, IBLOCK, INDEXW, GERS, Z, LDZ, ISUPPZ, WORK, IWORK, INFO)
	   SLARRV computes the eigenvectors of the tridiagonal matrix T = L D LT given L, D and
	   the eigenvalues of L D LT.

Function/Subroutine Documentation
   subroutine slarrv (integerN, realVL, realVU, real, dimension( * )D, real, dimension( * )L,
       realPIVMIN, integer, dimension( * )ISPLIT, integerM, integerDOL, integerDOU, realMINRGP,
       realRTOL1, realRTOL2, real, dimension( * )W, real, dimension( * )WERR, real, dimension( *
       )WGAP, integer, dimension( * )IBLOCK, integer, dimension( * )INDEXW, real, dimension( *
       )GERS, real, dimension( ldz, * )Z, integerLDZ, integer, dimension( * )ISUPPZ, real,
       dimension( * )WORK, integer, dimension( * )IWORK, integerINFO)
       SLARRV computes the eigenvectors of the tridiagonal matrix T = L D LT given L, D and the
       eigenvalues of L D LT.

       Purpose:

	    SLARRV computes the eigenvectors of the tridiagonal matrix
	    T = L D L**T given L, D and APPROXIMATIONS to the eigenvalues of L D L**T.
	    The input eigenvalues should have been computed by SLARRE.

       Parameters:
	   N

		     N is INTEGER
		     The order of the matrix.  N >= 0.

	   VL

		     VL is REAL

	   VU

		     VU is REAL
		     Lower and upper bounds of the interval that contains the desired
		     eigenvalues. VL < VU. Needed to compute gaps on the left or right
		     end of the extremal eigenvalues in the desired RANGE.

	   D

		     D is REAL array, dimension (N)
		     On entry, the N diagonal elements of the diagonal matrix D.
		     On exit, D may be overwritten.

	   L

		     L is REAL array, dimension (N)
		     On entry, the (N-1) subdiagonal elements of the unit
		     bidiagonal matrix L are in elements 1 to N-1 of L
		     (if the matrix is not splitted.) At the end of each block
		     is stored the corresponding shift as given by SLARRE.
		     On exit, L is overwritten.

	   PIVMIN

		     PIVMIN is REAL
		     The minimum pivot allowed in the Sturm sequence.

	   ISPLIT

		     ISPLIT is INTEGER array, dimension (N)
		     The splitting points, at which T breaks up into blocks.
		     The first block consists of rows/columns 1 to
		     ISPLIT( 1 ), the second of rows/columns ISPLIT( 1 )+1
		     through ISPLIT( 2 ), etc.

	   M

		     M is INTEGER
		     The total number of input eigenvalues.  0 <= M <= N.

	   DOL

		     DOL is INTEGER

	   DOU

		     DOU is INTEGER
		     If the user wants to compute only selected eigenvectors from all
		     the eigenvalues supplied, he can specify an index range DOL:DOU.
		     Or else the setting DOL=1, DOU=M should be applied.
		     Note that DOL and DOU refer to the order in which the eigenvalues
		     are stored in W.
		     If the user wants to compute only selected eigenpairs, then
		     the columns DOL-1 to DOU+1 of the eigenvector space Z contain the
		     computed eigenvectors. All other columns of Z are set to zero.

	   MINRGP

		     MINRGP is REAL

	   RTOL1

		     RTOL1 is REAL

	   RTOL2

		     RTOL2 is REAL
		      Parameters for bisection.
		      An interval [LEFT,RIGHT] has converged if
		      RIGHT-LEFT.LT.MAX( RTOL1*GAP, RTOL2*MAX(|LEFT|,|RIGHT|) )

	   W

		     W is REAL array, dimension (N)
		     The first M elements of W contain the APPROXIMATE eigenvalues for
		     which eigenvectors are to be computed.  The eigenvalues
		     should be grouped by split-off block and ordered from
		     smallest to largest within the block ( The output array
		     W from SLARRE is expected here ). Furthermore, they are with
		     respect to the shift of the corresponding root representation
		     for their block. On exit, W holds the eigenvalues of the
		     UNshifted matrix.

	   WERR

		     WERR is REAL array, dimension (N)
		     The first M elements contain the semiwidth of the uncertainty
		     interval of the corresponding eigenvalue in W

	   WGAP

		     WGAP is REAL array, dimension (N)
		     The separation from the right neighbor eigenvalue in W.

	   IBLOCK

		     IBLOCK is INTEGER array, dimension (N)
		     The indices of the blocks (submatrices) associated with the
		     corresponding eigenvalues in W; IBLOCK(i)=1 if eigenvalue
		     W(i) belongs to the first block from the top, =2 if W(i)
		     belongs to the second block, etc.

	   INDEXW

		     INDEXW is INTEGER array, dimension (N)
		     The indices of the eigenvalues within each block (submatrix);
		     for example, INDEXW(i)= 10 and IBLOCK(i)=2 imply that the
		     i-th eigenvalue W(i) is the 10-th eigenvalue in the second block.

	   GERS

		     GERS is REAL array, dimension (2*N)
		     The N Gerschgorin intervals (the i-th Gerschgorin interval
		     is (GERS(2*i-1), GERS(2*i)). The Gerschgorin intervals should
		     be computed from the original UNshifted matrix.

	   Z

		     Z is REAL array, dimension (LDZ, max(1,M) )
		     If INFO = 0, the first M columns of Z contain the
		     orthonormal eigenvectors of the matrix T
		     corresponding to the input eigenvalues, with the i-th
		     column of Z holding the eigenvector associated with W(i).
		     Note: the user must ensure that at least max(1,M) columns are
		     supplied in the array Z.

	   LDZ

		     LDZ is INTEGER
		     The leading dimension of the array Z.  LDZ >= 1, and if
		     JOBZ = 'V', LDZ >= max(1,N).

	   ISUPPZ

		     ISUPPZ is INTEGER array, dimension ( 2*max(1,M) )
		     The support of the eigenvectors in Z, i.e., the indices
		     indicating the nonzero elements in Z. The I-th eigenvector
		     is nonzero only in elements ISUPPZ( 2*I-1 ) through
		     ISUPPZ( 2*I ).

	   WORK

		     WORK is REAL array, dimension (12*N)

	   IWORK

		     IWORK is INTEGER array, dimension (7*N)

	   INFO

		     INFO is INTEGER
		     = 0:  successful exit

		     > 0:  A problem occured in SLARRV.
		     < 0:  One of the called subroutines signaled an internal problem.
			   Needs inspection of the corresponding parameter IINFO
			   for further information.

		     =-1:  Problem in SLARRB when refining a child's eigenvalues.
		     =-2:  Problem in SLARRF when computing the RRR of a child.
			   When a child is inside a tight cluster, it can be difficult
			   to find an RRR. A partial remedy from the user's point of
			   view is to make the parameter MINRGP smaller and recompile.
			   However, as the orthogonality of the computed vectors is
			   proportional to 1/MINRGP, the user should be aware that
			   he might be trading in precision when he decreases MINRGP.
		     =-3:  Problem in SLARRB when refining a single eigenvalue
			   after the Rayleigh correction was rejected.
		     = 5:  The Rayleigh Quotient Iteration failed to converge to
			   full accuracy in MAXITR steps.

       Author:
	   Univ. of Tennessee

	   Univ. of California Berkeley

	   Univ. of Colorado Denver

	   NAG Ltd.

       Date:
	   September 2012

       Contributors:
	   Beresford Parlett, University of California, Berkeley, USA
	    Jim Demmel, University of California, Berkeley, USA
	    Inderjit Dhillon, University of Texas, Austin, USA
	    Osni Marques, LBNL/NERSC, USA
	    Christof Voemel, University of California, Berkeley, USA

       Definition at line 280 of file slarrv.f.

Author
       Generated automatically by Doxygen for LAPACK from the source code.

Version 3.4.2				 Tue Sep 25 2012			      slarrv.f(3)
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